Table 1.

Effect of enrichment for biomarker-positive cases on the probability of falsely concluding that a new therapy increases the response rate when a single-arm phase II study is designed using assumptions from an unselected population

Historical response rate in the unselected population (%)Historical response rate in the subpopulation enriched for biomarker-positive cases (%)Sample sizeNo. observed responses required to conclude that the response rate is increased by the new therapyActual probability of falsely concluding that the new therapy increases the response rate in the enriched subpopulation
10153060.29
10203060.57
202536110.27
203036110.53
303539160.26
304039160.51
  • NOTE: Single-arm phase II studies are typically designed to test against benchmark historical response rates in the range of the example rates provided in column 1. When the historical response rate in the subpopulation enriched for biomarker-positive cases is unknown, it is often assumed to be the same as in the unselected population. Column 2 presents the (unknown) historical response rate in the subset of patients who are positive for the biomarker. Sample size (column 3) and required observed response rate (column 4) are calculated to satisfy two conditions: (a) control the probability of falsely concluding that the true response rate has been increased from the historical rate in the unselected population to be ≤0.10 and (b) provide at least 0.90 probability of concluding that the new therapy has increased the response rate when the new therapy has a true response rate that represents an absolute increase of 20% compared with the historical response rate in the unselected population.